The present invention relates to a display of general three-dimensional digital data and more particularly, to a method and apparatus for displaying multi-valued component data by use of tensor rendering, which can be used, e.g., for applications which follow.
(1) General tensor scientific data analysis;
(2) Statistical data analysis using a multi-value function;
(3) Representation of metallic texture in computer graphics; and
(4) Internal structure diagnosis using a magnetic resonance imaging (MRI) apparatus.
As a prior art for visually displaying a scalar field, there is a scalar volume rendering method (refer to JP-B-7-27576 by Pixar Ltd.). In a three-dimensional shape displaying method used in an ordinary computer graphics, for the purpose of displaying a three-dimensional scalar field by providing spatial coordinate points such as apexes of a three-dimensional figure and by geometrically displaying a polyhedron, it is necessary as its pre-stage to determine an isosurface (iso-density surface, iso-pressure surface, etc.) corresponding to a two-dimensional contour line.
That is, the scalars of three-dimensional lattice points are given to calculate coordinate data including the apexes, ridge lines and face orientations of polygons of isosurface in a three-dimensional space, and resultant polyhedron data are hidden-surface-processed for display. In the scalar volume rendering method, on the other hand, a radiative transfer equation is approximately solved to represent the concentration of a spatial density without determining the surfaces of a three-dimensional figure.
This method which represents a shape as a degree of opacity is featured in that since the operation of determining an isosurface involves no data round-down based on a threshold, the quality of input data reflects on the quality of a display image as it is. However, this method uses only a radiation-transportation model of a scattering light for relating a single function to opacity or color and uses no such a scattering light model as able to cope with multi-valued component data of a multi-value function. For this reason, for displaying the multi-valued component data, the method requires not only the repetition of volume-rendering-calculation for each of the multi-valued component data, demanding a massive amount of calculation, but also a post-processing for comparison of an image to be displayed.
Another prior art method for displaying multi-valued component data of a multi-value function is a method for displaying a three-dimensional icon (see IEEE Visualization 93, pp.39-45) as an image. In this method, a distribution of three-dimensional multi-valued component data is displayed by displaying as an image the situation in which a three-dimensional icon object having a freedom of shape corresponding to the multi-valued component data is positioned in a space. However, since the shape of the three dimensional icon object becomes complicated, a limited resolution of display screen disables simultaneous display of a multiplicity of sampling points.
As a result, the multi-valued component data to be displayed are selected, undesirably leading to display of only part of the data to be analyzed.
Another prior art method for displaying multi-valued component data of a multi-value function is a method for simultaneously displaying five three-dimensional components (see IEEE Visualization 97, pp.479-482). In this method, not tensors but two types of scalars and one type of vector are overwritten, and an geometrical object is utilized. Thus, this method is limited to applications where it is desired to display a small number of sampling points.
Also suggested is a method for displaying three-dimensional tensor components (see IEEE Visualization 97, pp.59-66). In this method, features are extracted from a distribution of nine components of a three dimensional tensor amount to three-dimensionally display its extracted result. This method, however, is suitable for such a purpose as to display the features of a multi-value function. However, this metod cannot be used for such a purpose as to detect fine defects from the entire multi-valued component data, because most of the data are subjected to the selecting operations prior to displaying.
The present invention may be applied to an internal structure diagnosis apparatus using a magnetic resonance imaging (MRI) system for a sample having a spin component.
In such MRI systems, there is already known a method for finding a diffusion tensor indicative of a displacement in the spin component of the sample based on a spin-echo intensity (see U.S. Pat. No. 5,539,310).
In ordinary MRI systems, since the applied electromagnetic pulse and the diffusion tensor component have a specific relationship therebetween, a three-dimensional tensor amount is output based on the magnetic resonance data measured in voxel unit.
However, in order to display the tensors of the three-dimensional diagnosis result, there has been conventionally used a method for two-dimensionally displaying only a partial section or a projection component.
In the conventional scalar volume rendering method, it has been difficult to grasp the correlation between multi-valued components in the component analysis based on reading of numeral value data, since the method displays only three dimensional one variable data.
The conventional method for displaying a three-dimensional icon as an image has a limit in resolution, because the method is of a geometrical figure display type based on sample extraction and cannot display all the data. Further, with respect to display, a polygon indicative of an icon has to be displayed in color and cannot be visualized on a monochrome display screen. Moreover, since shading is used regardless of display information, multi-valued components having a large value change range cannot be undesirably displayed.
The present invention has five objects that provide a method and apparatus for displaying high-dimensional (e.g., three-dimensional) digital data by use of tensor rendering which has the following functions and effects (1) to (5).
(1) Component correlation can be easily grasped by providing a user interface for diagnostic analysis of multi-valued component data and by providing such display as to directly appeal to human vision, such as emphasized display of featured locations;
(2) Lack and Missing of multi-valued component data analysis can be prevented to improve an efficiency in the entire data analysis;
(3) A tensor distribution over an entire three-dimensional space can be visualized;
(4) Display is carried out in conformity with tensor characteristics for use as general input data of scientific computation; and
(5) High-speed display can be realized by parallel-processing the rendering computation for displaying.
To attain the above first to fifth objects and correspondingly obtain the above functions and effects (1) to (5), the following means (a) to (e) are provided.
(a) For the purpose of realizing three-dimensional image display to allow an observer to conduct the data diagnosis by a technique for visualizing a distribution of components in a space, the anisotropic scattering of light permeated and absorbed is used, as an index of multi-valued information diagnosis.
(b) Since it is difficult to directly represent a large amount of sampling points in the form of a geometrical figure, a multi-valued component input is normalized into an opacity distribution and its optical attributes. A space is defined as a set of small fine faces having opacity, brightness and scattering vectors, and light absorbed and scattered on the faces are numerically calculated.
In FIG. 1, more specifically, a very small virtual face distribution 102 having an anisotropy is corresponded on a discrete sample region unit 103 having tensor amount. A shape of a very small face distribution function 101 necessary for simulation of light scattering by the very small virtual face distribution 102 having an anisotropy is assumed as two-order curved surface of an anisotropic ellipsoid. An intensity of the scattering light is calculated based on a contribution of a vector 107 directed to a direction of a bisector between a light-source-directed vector 105 and a line of sight vector (view direction vector) 106.
(c) To specify multi-valued components representing an opacity, it is assumed as an opacity control principle of tensor rendering that light passed through an anisotropic ellipsoid is absorbed according to its optical path length.
With respect to each computation point having a tensor, the intensity of the absorbed light is integrated according to the following rendering light beam equation (Equation 5), the transmittance of the scattering light is weighted.                               xe2x80x83                ⁢                                            C              λ                        ⁢                          xe2x80x83                        ⁢                          (                              u                i                            )                                =                                    ∑                              k                =                0                            k                        ⁢                          xe2x80x83                        ⁢                          [                                                c                  λ                                ⁢                                  xe2x80x83                                ⁢                                  (                                      x                    k                                    )                                ⁢                                  xe2x80x83                                ⁢                α                ⁢                                  xe2x80x83                                ⁢                                  (                                                            u                      i                                        ,                                          x                      k                                                        )                                ⁢                                                      ∏                                          m                      =                                              k                        +                        1                                                              k                                    ⁢                                      xe2x80x83                                    ⁢                                      (                                          1                      -                                              α                        ⁢                                                  xe2x80x83                                                ⁢                                                  (                                                                                    u                              i                                                        ,                                                          x                              k                                                                                )                                                                                      )                                                              ]                                                          (                  Equation          ⁢                      xe2x80x83                    ⁢          5                )            
The rendering integration causes nine tensor components of each point in the space to be output to a display image as light information.
(d) Mapping of a tensor type of three-dimensional multi-valued component input data is carried out by sorting the input data into the symmetrical tensor components and the anti-symmetrical tensor components (or by splitting or decomposing the input data, if the sorting is impossible).
(e) For speeding up of the tensor rendering, parallel control is employed. The light simulation computation (especially, rendering light beam integration) can be subjected to the parallel operation, whereby the expandability of resolution and so forth can also be secured.